SAT Math Multiple Choice Question 145: Answer and Explanation

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Question: 145

10. Shaun is developing a weight loss regimen, which includes both a workout plan and a calorie-restriction plan. Shaun wants to work out for no less than 30 minutes and no more than 60 minutes a day and consume no less than 2,000 and no more than 2,500 calories. If each minute, m, of his workout time burns 50 calories, which of the following inequalities represents the number of minutes, m, that Shaun can work out each day to burn off as many calories as he consumes?

  • A. 30 ≤ m ≤ 60
  • B. 30 ≤ m ≤ 50
  • C. 40 ≤ m < 50
  • D. 40 ≤ m ≤ 50

Correct Answer: D

Explanation:

D If each minute of his workout time burns 50 calories, and he wants to consume no fewer than 2,000 calories, Shaun must work out for a minimum of = 40 minutes. If he wants to consume no more than 2,500 calories, Shaun must work out for a maximum of = 50 minutes. Since the question asks for the inequality that represents the number of minutes for which Shaun will burn off as many calories as he consumes, (D) is correct, as it includes both the minimum (40 minutes) and maximum (50 minutes) amount of time that he can work out. Choice (C) is incorrect because the answer should include 50 (he can work out for a "maximum" of 50 minutes, so he could work out for 50 minutes), but the lesser than sign ("<") excludes 50.

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